Abstract
The paper introduces a general class of neural networks with periodic inputs. By constructing a Lyapunov functional and the Halanay-type inequality separately, we obtain easily verifiable sufficient conditions ensuring that every solutions of the delayed neural networks converge exponentially to the unique periodic solutions. The results obtained can be regarded as a generalization to the discrete case of previous results.
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Bouzerman, A., Pattison, T.: Neural Network for Quadratic Optimization with Bound Constraints. IEEE Trans. Neural Networks 4, 293–303 (1993)
Forti, M., Nistri, P.: Global Convergence of Neural Networks with Discontinuous Neuron Activations. IEEE Trans. Circuits and Systems I 50(11), 1421–1435 (2003)
Forti, M., Tesi, A.: New Conditions for Global Stability of Neural Networks with Application to Linear and Quadratic Programming Problems. IEEE Trans. Circuits and Systems I 42, 354–366 (1995)
Venetianer, P., Roska, T.: Image Compression by Delayed CNNs. IEEE Trans. Circuits Syst. I 45, 205–215 (1998)
Sun, C., Feng, C.: Neural Networks for Nonconvex Nonlinear Programming Problems: A Switching Control Approach. In: Wang, J., Liao, X.-F., Yi, Z. (eds.) ISNN 2005. LNCS, vol. 3496, pp. 694–699. Springer, Heidelberg (2005)
Morita, M.: Associative Memory with Non-montone Dynamics. Neural networks 6, 115–126 (1993)
Tank, D., Hopfield, J.: Simple “Neural” Optimization Networks: An A/D Converter, Signal Decision Circuit, And A Linear Programming Circuit. IEEE Trans. Circuits & Systems 33, 533–541 (1996)
Kennedy, M., Chua, L.: Neural Networks for Linear and Nonlinear Programming. IEEE Trans. Circuits & Systems 35, 554–562 (1988)
Liao, X., Wong, K., Yang, S.: Convergence Dynamics of Hybrid Bidirectional Associative Memory Neural Networks with Distributed Delays. Physics Letters A 316, 55–64 (2003)
Cao, J., Wang, J.: Global Asymptotic Stability of Recurrent Neural Networks with Lipschitz-continuous Activation Functions and Time-Varying Delays. IEEE Trans. Circuits Syst. I 50, 34–44 (2003)
Liao, X., Wang, J.: Algebraic Criteria for Global Exponential Stability of Cellular Neural Networks with Multiple Time Delays. IEEE Trans. Circuits Systems I 50(2), 268–275 (2003)
Sun, C., Feng, C.: Exponential Periodicity of Continuous-time And Discrete-time Neural Networks with Delays. Neural Processing Letters 19(2), 131–146 (2004)
Sun, C., Feng, C.: On Robust Exponential Periodicity of Interval Neural Networks with Delays. Neural Processing Letters 20(1), 53–61 (2004)
Sun, C., Feng, C.: Exponential Periodicity And Stability of Delayed Neural Networks. Mathematics and Computers in Simulation 66, 469–478 (2004)
Sun, C., Zhang, K., Fei, S., Feng, C.: On Exponential Stability of Delayed Neural Networks with A General Class of Activation Functions. Physics Letters A 298, 122–132 (2002)
Sun, C., Feng, C.: Global Robust Exponential Stability of Interval Neural Networks with Delays. Neural Processing Letters 17(1), 107–115 (2003)
Zhang, J., Jin, X.: Global Stability Analysis in Delayed Hopfield Neural Network Models. Neural Networks 13, 745–753 (2000)
Wang, L.: Stability of Cohen–Grossberg Neural Networks with Distributed Delays. Applied Mathematics and Computation 160, 93–110 (2005)
Zeng, Z., Wang, J., Liao, X.: Global Exponential Stability of A General Class of Recurrent Neural Networks with Time-Varying Delays. IEEE Trans. Circuits System I 50, 1353–1359 (2003)
Yi, Z., Tan, K.: Convergence Analysis of Recurrent Neural Networks. Kluwer Academic Publishers, Dordrecht (2003)
Mohamad, S.: Global Exponential Stability in Continuous-time And Discrete-time Delay Bi-directional Neural Networks. Physical D 159, 233–251 (2001)
Mohamad, S., Gopalsamy, K.: Exponential Stability of Continuous-time And Discrete-time Cellular Neural Networks with Delays. Applied Mathematics and Computation 135, 17–38 (2003)
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Sun, C., Li, L. (2006). Dynamics of General Neural Networks with Distributed Delays. In: Wang, J., Yi, Z., Zurada, J.M., Lu, BL., Yin, H. (eds) Advances in Neural Networks - ISNN 2006. ISNN 2006. Lecture Notes in Computer Science, vol 3971. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11759966_20
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DOI: https://doi.org/10.1007/11759966_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34439-1
Online ISBN: 978-3-540-34440-7
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